Warping Function Statistics

Compute summary statistics for a collection of warping functions from a Karcher mean computation, including the mean warp, variance, standard deviation bands, and geodesic distances.

Usage

warp.statistics(karcher.result)

Arguments

karcher.result

An object of class karcher.mean.

Value

An object of class warp.statistics with components:

mean

Mean warping function

variance

Pointwise variance of warps

std.dev

Pointwise standard deviation of warps

lower.band

Lower confidence band (mean - 2 SD)

upper.band

Upper confidence band (mean + 2 SD)

karcher.mean.warp

Karcher mean of warps in geodesic space

geodesic.distances

Geodesic distances of each warp from identity

call

The matched call

References

Srivastava, A. and Klassen, E. (2016). Functional and Shape Data Analysis. Springer.

See also

karcher.mean, phase.boxplot

Examples

# \donttest{
set.seed(1)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 15, 50)
for (i in 1:15) X[i, ] <- sin(2 * pi * (t - i / 60))
fd <- fdata(X, argvals = t)
km <- karcher.mean(fd, max.iter = 5)
ws <- warp.statistics(km)
ws
#> Warping Function Statistics
#>   Grid points: 50 
#>   Curves: 15 
#>   Mean geodesic distance: 0.1262 
#>   Max geodesic distance: 0.2318 
# }